A CP formulation for scheduling multiproduct multistage batch plants

The short-term scheduling of multiproduct multistage batch plants is tackled in this paper by means of a constraint programming (CP) methodology. This approach, consisting of both a model and a search strategy, easily handles different features found in industrial environments: finite unit ready times, dissimilar parallel equipment at each stage, sequence-dependent changeovers, topology constraints, forbidden job-equipment assignments, order release times, as well as renewable resources limitations. It can also address various interstage storage and operational policies: UIS, NIS/ZW, NIS/UW, and mixed ones. Besides, it introduces two simple and efficient search methodologies based on domain knowledge, whose great impact on the computational performance is shown. The approach was extensively tested by means of several examples having various difficulty degrees. It rendered good computational results for a variety of interstage storage policies and objective functions. Moreover, this work shows that the default depth-first search strategy does not perform well for scheduling problems.     

Scheduling multistage, multiproduct batch plants with nonidentical parallel units and unlimited intermediate storage

Scheduling production optimally in multistage multiproduct plants with nonidentical parallel units is a very difficult but routine problem that has received limited attention. In this paper, we construct, analyze, and rigorously compare a variety of novel mixed-integer linear programming formulations using unit-slots, stage-slots, process-slots, a variety of slot arrangements and sequence-modeling techniques, 4-index and 3-index binary variables, etc. While two of our 4-index models are an order of magnitude faster than existing models on 22 test problems of varying sizes, we find that no single model performs consistently the best for all problems. Our work suggests that the best strategy for solving difficult scheduling problems may be to use a set of competitive models in parallel and terminate them all, when one of them achieves the desired solution. We also develop several heuristic models based on our formulations and find that even a heuristic based on an inferior model can surpass others based on superior models. Thus, it may not always be wise to just aim for a single best model for a given scheduling problem, but a host of novel and competitive models, as we have done in this paper.     

Development of a batch manager for dynamic scheduling and process management in multiproduct batch processes

A batch manager is developed for the dynamic scheduling and on-line management of process operations. The developed system consists of a process monitoring module and a dynamic scheduling module. When a deviation from the initial schedule is detected in a process monitoring module, dynamic scheduling is performed in the dynamic scheduling module and the initial schedule is adjusted to the proper schedule by using rescheduling algorithms presented in this paper. The adjusted schedule is shown in the process monitoring module. The dynamic scheduler in the batch manager copes with several unexpected process events of batch process operations by adjusting the EST (Earliest Start Time) of equipment, redetermining the batch path and reassigning tasks to equipment. This study focuses on the implementation of a batch manager with on-line dynamic scheduling for batch process management. Examples of fodder production batch processes illustrate the efficiency of the algorithms. This paper was supported by nondirected research fund, Korea Research Foundation, 1997.     

Integrated production planning and scheduling using a decomposition framework

To ensure the consistency between planning and scheduling decisions, the integrated planning and scheduling problem should be addressed. Following the natural hierarchy of decision making, integrated planning and scheduling problem can be formulated as bilevel optimization problem with a single planning problem (upper level) and multiple scheduling subproblems (lower level). Equivalence between the proposed bilevel model and a single level formulation is proved considering the special structure of the problem. However, the resulting model is still computationally intractable because of the integrality restrictions and large size of the model. Thus a decomposition based solution algorithm is proposed in this paper. In the proposed method, the production feasibility requirement is modeled through penalty terms on the objective function of the scheduling subproblems, which is further proportional to the amount of unreachable production targets. To address the nonconvexity of the production cost function of the scheduling subproblems, a convex polyhedral underestimation of the production cost function is developed to improve the solution accuracy. The proposed decomposition framework is illustrated through examples which prove the effectiveness of the method.     

Optimal production sequence and processing schedules of multiproduct batch processes for heat integration and minimum equipment costs

The production sequence and the processing schedules of multiproduct batch processes can be changed for maximum heat recovery and minimum equipment costs between batch streams. However, the modified production sequence and processing schedule may increase the production cycle time, which causes the bigger equipment sizes required in batch processes. In this study, the required equipment sizes, the production sequence and the processing times of the multiproduct batch processes are mathematically formulated for maximum heat integration and low equipment costs in a mixed integer nonlinear programming. The optimal solution of this formulation was obtained by GAMS/DICOPT programming solver. Examples are presented to show the capabilities of the model.     

A multiscale mass transfer model for gas-solid riser flows: Part II—Sub-grid simulation of ozone decomposition

This article is to test the EMMS-based multiscale mass transfer model through computational fluid dynamics (CFD) simulation of ozone decomposition in a circulating fluidized bed (CFB) reactor. Three modeling approaches, namely types A, B and C, are classified according to their drag coefficient closure and mass transfer equations. Simulation results show that the routine approach (type C) with assumption of homogeneous flow and concentration overestimates the ozone conversion rate, introduction of structure-dependent drag force will improve the model prediction (type B), while the best fit to experimental data is obtained by the multiscale mass transfer approach (type A), which takes into account the sub-grid heterogeneity of both flow and concentration. In general, multiscale behavior of mass transfer is more distinct especially for the dense riser flow. The fair agreement between our new model with literature data suggests a fresh paradigm for the CFB related reaction simulation.     

A new Lagrangian decomposition approach applied to the integration of refinery planning and crude-oil scheduling

The aim of this paper is to introduce a methodology to solve a large-scale mixed-integer nonlinear program (MINLP) integrating the two main optimization problems appearing in the oil refining industry: refinery planning and crude-oil operations scheduling. The proposed approach consists of using Lagrangian decomposition to efficiently integrate both problems. The main advantage of this technique is to solve each problem separately. A new hybrid dual problem is introduced to update the Lagrange multipliers. It uses the classical concepts of cutting planes, subgradient, and boxstep. The proposed approach is compared to a basic sequential approach and to standard MINLP solvers. The results obtained on a case study and a larger refinery problem show that the new Lagrangian decomposition algorithm is more robust than the other approaches and produces better solutions in reasonable times.     

A novel MILP formulation for short-term scheduling of multi-stage multi-product batch plants with sequence-dependent constraints

This paper presents a continuous-time mixed-integer linear programming (MILP) model for short-term scheduling of multi-stage multi-product batch plants. The model determines the optimal sequencing and the allocation of customer orders to non-identical processing units by minimizing the earliness and tardiness of order completion. This is a highly combinatorial problem, especially when sequence-dependent relations are considered such as the setup time between consecutive orders. A common approach to this scheduling problem relies on the application of tetra-index binary variables, i.e. (order, order, stage, unit) to represent all the combinations of order sequences and assignments to units in the various stages. This generates a huge number of binary variables and, as a consequence, much time is required for solutions. This paper proposes a novel formulation that replaces the tetra-index binary variables by one set of tri-index binary variables (order, order, stage) without losing the model's generality. By the elimination of the unit index, the new formulation requires considerably fewer binary variables, thus significantly shortening the solution time.     

A projection‐based method for production planning of multiproduct facilities

An algorithm is presented for identifying the projection of a scheduling model's feasible region onto the space of production targets. The projected feasible region is expressed using one of two mixed‐integer programming formulations, which can be readily used to address integrated production planning and scheduling problems that were previously intractable. Production planning is solved in combination with a surrogate model representing the region of feasible production amounts to provide optimum production targets, while a detailed scheduling is solved in a rolling‐horizon manner to define feasible schedules for meeting these targets. The proposed framework provides solutions of higher quality and yields tighter bounds than previously proposed approaches. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

A novel precedence-based and heuristic approach for short-term scheduling of multipurpose batch plants

Many continuous-time formulations have been proposed during the last decades for short-term scheduling of multipurpose batch plants. Although these models establish advantages over discrete-time representations, they are still inefficient in solving moderate-size problems, such as maximization of profit in long horizon, and minimization of makespan. Unlike existing literature, this paper presents a new precedence-based mixed integer linear programming (MILP) formulation for short-term scheduling of multipurpose batch plants. In the new model, multipurpose batch plants are described with a modified state-task network (STN) approach, and binary variables express the assignments and sequences of batch processing and storing. To eliminate the drawback of precedence-based formulations which commonly include large numbers of batches, an iterative procedure is developed to determine the appropriate number of batch that leads to global optimal solution. Moreover, four heuristic rules are proposed to selectively prefix some binary variables to 0 or 1, thereby reducing the overall number of binary variables significantly. To evaluate model performance, our model and the best models reported in the literature (S&K model and I&F model) are utilized to solve several benchmark examples. The result comparison shows that our model is more effective to find better solution for complex problems when using heuristic rules. Note that our approach not only can handle unlimited intermediate storage efficiently as well as the I&F model, but also can solve scheduling problems in limited intermediate storage more quickly than the S&K model.     

A new multiscale modeling approach for the prediction of mechanical properties of polymer-based nanomaterials

A detailed knowledge about the physics and chemistry of multiphase materials on different length and time scales is essential to tailor their macroscopic physical and mechanical properties. A better understanding of these issues is also highly relevant to optimize their processing and, thus, their elucidation can be decisive for their final industrial application. In this paper, we develop a new multiscale modeling method, which combines the self-consistent field theory approach with the kinetic Monte Carlo method, to simulate the structural–dynamical evolution taking place in thermoplastic elastomers, where hard glassy and soft rubbery phases alternate. Since the early seventies, it is well established that the properties of the core nanophases in these multiphase materials considerably affect their overall mechanical properties. However, recent experimental studies have clearly demonstrated that, besides the efficient handling of the core nanophases, the appropriate treatment of their interfacial region is another major challenge one has to face on the way of target-oriented development of these materials. In this work, we set a particular focus on the complex structural–dynamical processes occurring at the interphases, and study their influence on the local structural and mechanical properties. To reach our objectives, we apply the new methodology on a thermoplastic elastomer composed of ABA triblock copolymers, subjected to a sizeable external perturbation, and determine its time-averaged internal stress and composition profile. We deduce from this investigation that, to obtain the correct local mechanical properties of these multiphase materials, their structure and dynamics need to be taken into account on an equal footing. Finally, our investigation also provides an explanation and confirms the importance of the chain-pullout mechanism in the viscoelastic and stress relaxation behavior of these materials.     

A method for flexibility analysis of continuous processing plants

A methodology has been developed for the analysis of operational flexibility of a continuous processing plant. An application has been demonstrated for a multipurpose plant with uncertain operating conditions. A practical flexibility analysis procedure using a direct search optimization algorithm is proposed to solve the problem. The method provides a heuristic screening technique that makes it possible to avoid the exhaustive enumeration of every constraint vertex, while the direct search optimization offers a simple and effective means to identify bottlenecks. A refinery multiperiod plant problem has been investigated in order to highlight the procedures which lead to the construction of flexibility indices for each operating mode.     

A multiscale modeling for predicting the thermal expansion behaviors of 3D C/SiC composites considering porosity and fiber volume fraction

Coefficients of thermal expansion (CTEs) are an essential design criterion of the three-dimensional carbon fiber reinforced SiC matrix composites (3D C/SiC). Representative volume element (RVE) models of microscale, void/matrix, and mesoscale developed in this work were used to investigate the CTEs of these composites. A coupled temp-displacement steady-state analysis step was created for assessing the thermal expansions behaviors of the composites by applying periodic displacement and temperature boundary conditions. Three RVE models of cuboid, hexagonal and fiber random distribution were respectively established to comparatively study the influence of fiber package pattern on the CTEs at microscale. Similarly, the effects of different void size, locations, and shapes on the CTEs of the matrix are comparatively analyzed by the void/matrix models. The prediction results at mesoscale corresponded closely to the experimental results. The effect of the porosities on the CTEs was studied by the void/matrix RVE models. The voids were effective in lowering the CTE of the 3D C/SiC composites. Furthermore, the effect of fiber volume fractions on the CTE were also taken into consideration. Equal in-plane and out-of-plane CTEs were realized by selecting appropriate fiber volume fractions for the different directions. The multiscale models developed in this work can be used to predict the thermal expansion behaviors of other complex structure composites.     

The integration of complete replanning and rule-based repairing for optimal operation of utility plants

The integration methodology of complete replanning and plan repairing is proposed to handle the prediction errors for energy demands during multiperiod operational planning. Complete replanning is implemented periodically and plan repairing is triggered during the execution interval. The plan repairing is constructed by a rule-based system because of real-time limitations. The efficiency index of a utility pump is introduced to determine startup/shutdown of equipment without integer programming in plan repairing. Case studies show that the proposed method is more profitable than the conventional replanning method. The total operating costs are reduced by 0.3-9.0% compared with the conventional replanning method.     

Sequential methodology for integrated optimization of energy and water use during batch process scheduling

Though commonly encountered in practice, energy and water minimization simultaneously during batch process scheduling has been largely neglected in literature. In this paper, we present a novel framework for incorporating simultaneous energy and water minimization in batch process scheduling. The overall problem is decomposed into three parts - scheduling, heat integration, and water reuse optimization - and solved sequentially. Our approach is based on the precept that in any production plant, utilities (energy and water) consumption is subordinate to the production target. Hence, batch scheduling is solved first to meet an economic objective function. Next, alternate schedules are generated through a stochastic search-based integer cut procedure. For each resulting schedule, minimum energy and water reuse targets are established and networks identified. As illustrated using two well-known case studies, a key feature of this approach is its ability to handle problems that are too complex to be solved using simultaneous methods.     

Role of the support and of the preparation method for copper-based catalysts in the 2-propanol decomposition

Pure copper oxide and mixed CuO/ZnO catalysts with different Cu:Zn atomic ratios were tested for the 2-propanol decomposition in order to investigate the nature of the active site and the role of the ZnO support. Fresh catalysts as well as catalysts oxidized in pure oxygen did not exhibit any catalytic activity below 373 K. When reduced either in pure hydrogen or in reaction mixture (helium plus alcohol) both copper oxide and mixed two-phase catalysts showed a dehydrogenating activity in the temperature range 323–423 K. The apparent activation energy for both reduced CuO and reduced CuO/ZnO catalysts was 60 ± 8 kJ mol^–1. The first order rate constants were found to be a linear function of the exposed zero-valent copper area. The comparison of Cu(0) turnover frequency in unsupported Cu(0) and in Cu(0)/ZnO samples did not show any synergic effect of the support. The role of the preparation method on the Cu(0) dispersion is also discussed.     

A novel thermal decomposition method for the synthesis of ZnO nanoparticles from low concentration ZnSO4 solutions

In this research work, ZnO nanoparticles were prepared by direct thermal decomposition method with Zn₄(SO₄)(OH)₆·0.5 H₂O as a precursor. The precursor was calcinated in air for 1 h at 825 °C. Samples were characterized by X-ray diffraction (XRD), energy dispersive spectroscopy (EDS), infrared spectrum (IR), and scanning electron microscopy (SEM), and transmission electron microscopy (TEM). The XRD, EDS, and IR results indicated that the ZnO nanoparticles were pure. The average crystallite and particle size of the ZnO nanoparticles were estimated to be 87 nm and 92 nm by XRD and TEM, respectively. The SEM and TEM images showed that the ZnO nanoparticles were of spherical shape. The simplicity of the present method suggests its potential application at industrial scale as a cheap and convenient way to produce pure ZnO nanoparticles from low concentration ZnSO₄ solutions.     

Effect of the precursor and the preparation method on copper based activated carbon catalysts for methanol decomposition to hydrogen and carbon monoxide

Copper oxide supported on activated carbon catalysts, obtained by various preparation techniques, are compared in methanol decomposition to hydrogen and carbon monoxide. The favourable role of copper deposition from ammonia solution of copper carbonate is proved. The effect of the preparation conditions on the catalysts activity and stability as well as on the nature of the catalytic active complexes is studied.